Nonlinear degenerate elliptic equations and axially symmetric problems

  • Joachim von Below
  • Helmut Kaul

Abstract.

We consider semilinear elliptic equations with a principal part degenerating on a boundary hyperplane. Weak existence, uniqueness and regularity of solutions are established by variational methods and by reduction to uniformly elliptic equations. An important application arises in the mathematical treatment of the rotating star problem in general relativity, where the axial symmetry admits the reduction of one of the Einstein equations to a problem of the above form on a meridian half plane.

AMS Subject Classification:35J20; 35J70 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim von Below
    • 1
  • Helmut Kaul
    • 2
  1. 1. Université du Littoral, LANGAL, Bâtiment Poincaré, 50, rue Ferdinand Buisson, B.P. 699, F-62228 Calais Cédex (France) FR
  2. 2. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen (Germany) DE

Personalised recommendations